Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.2Subtraction Equations

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve one-step addition and subtraction equations using inverse operations.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. x + 25 = 60 — both sides equal 60 when x = 35
Inverse operationSpanish: Operación inversa Two math actions that undo each other, like × and ÷. − and +
IsolateSpanish: Despejar To get the letter by itself on one side. get m by itself
SolutionSpanish: Solución A number that makes the equation or inequality true. m = 23 checks out
One-step equationSpanish: Ecuación de un paso An equation you can solve in a single step using one inverse operation. x + 4 = 9 is solved in one step: subtract 4 from both sides, so x = 5.
BalanceSpanish: Equilibrio Keeping both sides of an equation equal by doing the same thing to each side. If you subtract 4 from the left side, you must subtract 4 from the right to keep balance.

How it worksWorked examplesolving a subtraction equation

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Sam gave away 18 marbles and had 27 left. Solve m − 18 = 27 for the marbles he started with.

  1. The variable side shows 18 subtracted from m, so the inverse move is addition.
  2. Add 18 to BOTH sides so the equation stays balanced.
  3. Left side: m − 18 + 18 leaves m. Right side: 27 + 18 gives 45.
  4. Check: 45 − 18 gives 27, so the value makes both sides equal.

Answer: m = 45, so Sam started with 45 marbles.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Rosa used 23 stickers and had 36 left. Solve y − 23 = 36 for the stickers she started with.

  1. What is done to y? is subtracted, so the inverse operation is .
  2. Do the same to each side: add to both sides.
  3. Left side leaves . Right side: 36 + 23 = .
  4. Check your value: − 23 = . Does it balance?
Answer:y = the stickers Rosa started with

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The variable has subtracted from it, so I to both sides.
  • I kept the equation balanced by .
  • My solution is because .
  • Subtraction and addition undo each other, so .

Word bank equationsubtractaddinverse operationisolatebalanceboth sidesdifferencesolutioncheckundo

Watch outA common mistake

A common mistake is applying the same operation instead of the inverse — for example, solving x − 7 = 15 by subtracting 7 from both sides (getting the wrong x = 8) instead of adding 7 to both sides (the correct x = 22). Another common mistake is doing the inverse operation to only one side, like solving x + 6 = 14 by subtracting 6 from the left but forgetting the right side. Before you submit, name the operation shown in the equation, choose its inverse, apply it to BOTH sides, and check by substituting your answer back into the original equation.

Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.2Subtraction Equations

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step addition and subtraction equations using inverse operations.

  1. 1Complete each step, then write the final answer.

    Solve n + 12 = 30.

    Show your work

    Hint 12 is added to n. Subtract 12 from both sides.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Solve x − 9 = 16.

    Show your work

    Hint 9 is subtracted from x. Add 9 to both sides.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve y + 21 = 50.

    Show your work

    Hint 21 is added to y. Subtract 21 from both sides.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.2Subtraction Equations

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step addition and subtraction equations using inverse operations.

  1. 1Complete each step, then write the final answer.

    Kai solved x − 12 = 30 and got x = 18. Is he right? What is x?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Solve m + 4.8 = 12.3.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve y + 35 = 62.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.2Subtraction Equations

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step addition and subtraction equations using inverse operations.

  1. 1Circle the letter of the best answer. Show how you know.

    Which value of n is the solution of n − 18 = 27?

    1. An = 9
    2. Bn = 18
    3. Cn = 27
    4. Dn = 45
    Show your work
  2. 2Complete each step, then write the final answer.

    Ana and Ben solve x + 9.5 = 20. Ana gets 10.5. Ben gets 29.5. What is x?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve n − 6.25 = 13.5.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help